Finite Group DatabasebetaFinite Group Databasebeta| order | 22599 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C81 · Schur multiplier (H2) = C33 |
| direct product | C3×C81×C31⋊C3 |
| Fitting | C3×C31×C81 ⋊ C3 |
| derived, Sylow | C31 ⋊ C32×C81 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C81 | C31⋊C3 |
| commutator, hypocenter | C31 | C32×C81 |
| Frattini | C27 | C32×C31⋊C3 |
| Fitting | C3×C31×C81 | C3 |
| socle | C32×C31 | C3×C27 |
| prime radical | C32×C31⋊C3 | C27 |
| cosocle | C27×C31 | C33 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C3×C81 | |
188 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7533 |
3159 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22599, 3081);